基于拓扑导数的复扩散在图像去噪及边缘提取中的应用

提出了基于拓扑导数的非线性复扩散用于图像去噪及边缘提取的一种算法.由于线性扩散会使图像边缘模糊,基于拓扑优化思想,对每个像素点的线性复扩散系数扰动,使得拓扑导数最小的扩散系数为最优.文中选取的扩散系数具有各向异性的特性,从而克服了Perona-Malik的各向同性扩散系数不利于去除边缘噪声的缺陷,选择拓扑导数足够小的像素点,对这些像素点用最优扩散系数进行扩散.文中给出了使算法迭代终止的判据.实验证明,与Guy Gilboa的非线性复扩散相比,本文方法对原始加噪图像处理后,实部图像体现出了更好的去噪效果,虚部图像则很好地保留了图像边缘,此外,本文方法还消除了Perona-Malik的方法对图像去噪后产生的阶梯效应.

Complex Diffusion Based on Topological Derivative for Image Denoising and Edge Extracting

An algorithm concerning application of nonlinear complex diffusion is presented based on topological optimization to image denoising and edge extracting.The linear diffusion blur edges,based on the idea of topological optimization,linear complex diffusion coefficients at each pixel are perturbed.It makes the lowest topological derivative to be optimum one.Diffusion coefficients have anisotropic property,thus overcoming the flaw of isotropic diffusion that cannot remove the noise along edges.Then,pixels with...